"AVG. serm. ed. Mai 161,4" is probably a reference to "Sermones S. Augustini ex codicibus Vaticanis," in Angelo Mai, Nova Patrum Bibliotheca (Rome, 1852), i, part I, pp. 1-470 (unavailable to me). I believe that many of these sermons attributed to St. Augustine in Mai's edition are now considered spurious.

Eric Thomson kindly copied and sent to me the following excerpt from Joshua Whatmough, The Dialects of Ancient Gaul: Prolegomena and Records of the Dialects (Cambridge: Harvard University Press, 1970), p. 220 (s.v. "branca, 'paw,' hence 'branch'"):

Apropos German 'zweig' for plough J.P. Mallory and D.Q. Adams, in their Oxford Introduction to Proto-European and the Proto-European World (Oxford: Oxford University Press, 2006), p. 156, draw attention to a host of words meaning 'forked branch' (in Gothic, Lithuanian, Russian, Armenian, Persian and Sanskrit) which developed the secondary meaning of plough (together with six examples from a different IE root also meaning branch which developed similarly) so even if biramica-branch is not to be credited there is nevertheless a sense of appropriate coincidence about it, as there is also about bracken-branch and bracchium-branch. Specious it may be but speciosus too, like kindred spirits no less kindred for lacking a common descent.

There are also some interesting remarks in Mallory and Adams about the use of metaphorical trees and branches to describe linguistic relationships. On pp. 2-3, they write:

But in the twelfth century a clever Icelandic scholar, considering these types of similarities, concluded that Englishmen and Icelanders 'are of one tongue, even though one of the two (tongues) has changed greatly, or both somewhat'. In a wider sense, the Icelander believed that the two languages, although they differed from one another, had 'previously parted or branched off from one and the same tongue'. The image of a tree with a primeval language as a trunk branching out into its various daughter languages was quite deliberatethe Icelander employed the Old Norse verb greina 'to branch'.

Id., pp. 71-72:

August Schleicher (1861-2) proposed one of the earliest models of the relationship between the various Indo-European groups (Fig. 5.1) that portrayed the groups as branches stemming from a common trunk (Stammbaum), and the concept of a family tree, although often maligned as oversimplistic, is still the primary method employed in indicating the interrelationships of the Indo-European languages.